Are there clever (fitness-based) crossover operators for binary chromosomes?
It's not obvious what you mean by "intelligent crossover".  

However, it is common to use fitness-based selection of parents: individuals in the current population who have higher fitness are assigned a higher probability of being selected to mate and produce offspring.  This will increase the likelihood that "good" combinations of genes in members of the current population will be passed along to the next generation, and that independent "good" combinations will be combined in some members of the next generation.

The "best" crossover operator depends dramatically on the structure of the problem being solved, and on the mapping of gene "vectors" to the salient features of a solution. 

Edit #1:
In some cases it is important to increase diversity in order to avoid convergence to a local optimum.  In that case, an "intelligent" GA might for example select a first parent for its high fitness, and a second parent at random.  In "Generator", a GA I sold for a while about 25 years ago, mate selection worked that way, and it was often very effective.  Generator also replaced any duplicate individuals in the population with entirely random individuals.  I have also structured genetic algorithms specifically to evolve multiple separate populations of individuals, with minimum gene flow between the populations, in order to evolve multiple solutions corresponding to "regional" fitness optima.

Edit #2:
In genetic algorithms it is not common to directly seek the best combination of genes from both parents. The assumption is that higher-fitness parents are more likely to produce even higher-fitness offspring than lower-fitness parents.  Sometimes there is a local search (hill climbing) operation where the offspring of two parents is mutated in various ways and the best of the mutants is put in the next generation.

And, sometimes a crossover operation involves producing a larger number of offspring than the parent generation, followed by culling low-fitness individuals to keep the population size constant.  This is vaguely analogous to a local search via mutation, but uses random crossover instead of random mutation for its search.